Coulomb Correlation Energy Research Articles

Oxygen on-site Coulomb energy in Pr1.3−xLa0.7CexCuO4 and Bi2Sr2CaCu2O8+δ and its relation with Heisenberg exchange

We study the electronic structure of electron-doped Pr$_{1.3-x}$La$_{0.7}$Ce$_{x}$CuO$_{4}$ (PLCCO ; $T_{c}$ = 27 K, x = 0.1) and hole-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi2212 ; $T_{c}$ = 90 K) cuprate superconductors using x-ray absorption spectroscopy (XAS) and resonant photoemission spectroscopy (Res-PES). From Res-PES across the O K-edge and Cu L-edge, we identify the O 2p and Cu 3d partial density of states (PDOS) and their correlation satellites which originate in two-hole Auger final states. Using the Cini-Sawatzky method, analysis of the experimental O 2p PDOS shows an oxygen on-site Coulomb energy for PLCCO to be $U_{p}$ = 3.3$\pm$0.5 eV and for Bi2212, $U_{p}$ = 5.6$\pm$0.5 eV, while the copper on-site Coulomb correlation energy, $U_{d}$ = 6.5$\pm$0.5 eV for Bi2212. The expression for the Heisenberg exchange interaction $J$ in terms of the electronic parameters $U_{d}$, $U_{p}$, charge-transfer energy $\Delta$ and Cu-O hopping $t_{pd}$ obtained from a simple Cu$_2$O cluster model is used to carry out an optimization analysis consistent with $J$ known from scattering experiments. The analysis also provides the effective one band on-site Coulomb correlation energy $\tilde{U}$ and the effective hopping $\tilde{t}$. PLCCO and Bi2212 are shown to exhibit very similar values of $\tilde{U}$/$\tilde{t}$ $\sim$9-10, confirming the strongly correlated nature of the singlet ground state in the effective one-band model for both the materials.

The Charge and Spin Thermoelectric Properties across Double Quantum Dots Serially Coupled to Ferromagnetic Leads: The Case of Parallel Magnetic Configuration

In this article, the charge and spin thermoelectric properties of double quantum dots system connected to ferromagnetic leads with collinear magnetic configurations will be studied in the linear response regime. Our results are calculated in a strong interdot coupling regime by taking into consideration all parameters affecting the system such as interaction between dots and their coupling to the leads, intradot Coulomb correlation energy and spin-polarization on the leads. It is found that in the parallel magnetic configuration, the thermoelectric efficiency can reach a large value around the spin-down resonance levels when the tunneling coupling between the quantum dots and the leads for the spin-down electrons are small, which leads to the pure spin Seebeck contribution. As a result, this system can generate a spin-polarized current. The value of the spin figure of merit is enhanced by increasing the spin-polarization and decreasing the correlation energy.

A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott–Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron–phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Pristine and oxidised Ag-nanoparticles on free-standing graphene as explored by X-ray photoelectron and Auger spectroscopy

Silver nanoparticles with a mean diameter of 15 nm have been grown on free-standing graphene and explored by soft X-ray synchrotron radiation using the ESCAmicroscopy beamline at Elettra. In particular, the 3d core orbitals and valence band (4d/5 s) of pristine and plasma-oxidised Ag-nanoparticles have been investigated by X-ray photoelectron spectroscopy (XPS), X-ray induced valence band photoemission, and MNN Auger spectroscopy. The X-ray spectra of the pristine Ag-nanoparticles, i.e. XPS, Auger and UPS spectra, are very similar to these of the metallic Ag-bulk film while the spectra of the oxidised Ag-nanoparticles exhibit distinct differences with respect to the oxidised Ag-bulk film. This is inferred from a larger valence band width, an extended valence band photoemission intensity nearly up to the Fermi level of the bulk metal, a smaller two-hole Coulomb correlation energy and a rather bulk-like Auger spectrum. We interpret this as to result from a shell-like composition of the Ag-nanoparticles with a thin passivating oxide layer and an inner metallic core. Moreover, the 3d photoemission peak of the oxidised nanoparticles is shifted to higher binding energy with respect to the bulk oxide peak. This is attributed not only to an XPS chemical shift but also to an additional final state Coulomb charging according to the electrostatic liquid drop model. Comparing the core binding energy shift of Ag-nanoparticles with the electrostatic potential of a spherical compact particle and a flat nanoislands a morphology transformation of the oxidised nanoparticles from 3D to 2D is obvious in the size range 5–15 nm.

Coulomb Energy Density Functionals for Nuclear Systems: Recent Studies of Coulomb Exchange and Correlation Functionals

The Coulomb exchange and correlation energy density functionals for electron systems are applied to nuclearsystems. It is found that the exchange functionals in the generalized gradient approximation provide agreements with the exact-Fock energy with one adjustable parameter within a few dozen keV accuracy, whereas the correlation functionals are not directly applicable to nuclear systems due to the existence of the nuclear force.

Application of a Coulomb energy density functional for atomic nuclei: Case studies of local density approximation and generalized gradient approximation

We test the Coulomb exchange and correlation energy density functionals of electron systems for atomic nuclei in the local density approximation (LDA) and the generalized gradient approximation (GGA). For the exchange Coulomb energies, it is found that the deviation between the LDA and GGA ranges from around $ 11 \, \% $ in $ {}^{4} \mathrm{He} $ to around $ 2.2 \, \% $ in $ {}^{208} \mathrm{Pb} $, by taking the Perdew-Burke-Ernzerhof (PBE) functional as an example of the GGA\@. For the correlation Coulomb energies, it is shown that those functionals of electron systems are not suitable for atomic nuclei.

The Electronic Structure Signature of the Spin Cross-Over Transition of [Co(dpzca)2

Abstract The unoccupied electronic structure of the spin crossover molecule cobalt (II) N-(2-pyrazylcarbonyl)-2-pyrazinecarboxamide, [Co(dpzca)2] was investigated, using X-ray absorption spectroscopy (XAS) and compared with magnetometry (SQUID) measurements. The temperature dependence of the XAS and molecular magnetic susceptibility χmT are in general agreement for [Co(dpzca)2], and consistent with density functional theory (DFT). This agreement of magnetic susceptibility and X-ray absorption spectroscopy provides strong evidence that the changes in magnetic moment can be ascribed to changes in electronic structure. Calculations show the choice of Coulomb correlation energy U has a profound effect on the electronic structure of the low spin state, but has little influence on the electronic structure of the high spin state. In the temperature dependence of the XAS, there is also evidence of an X-ray induced excited state trapping for [Co(dpzca)2] at 15 K.

Magnetic Susceptibility and Neutron Scattering of Graphene in Antiferromagnetic State: a Tight-Binding Approach

We address here a tight-binding model study of the frequency-dependent antiferromagnetic spin susceptibility for the graphene systems. The Hamiltonian consists of electron hopping up to the third-nearest-neighbors, substrate and impurity effects in presence of electron-electron interactions at A and B sub-lattices. To calculate susceptibility, we evaluate the two-particle electron Green’s function by using Zubarev’s Green’s function technique. The frequency-dependent antiferromagnetic susceptibility of the system is computed numerically by taking 1000 X 1000 grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher-energy peak associated with the substrate-induced gap. The evolution of these two peaks are investigated by varying neutron wave vector, Coulomb correlation energy, substrate-induced gap, electron hopping integrals and A- and B-site electron-doping concentrations.

Microscopic theory of substrate-induced gap effect on real AFM susceptibility in graphene

We address here a tight-binding model study of frequency-dependent real part of antiferromagnetic susceptibility for the graphene systems. The Hamiltonian consists of electron hopping upto third nearest-neighbours, substrate and impurity effects in the presence of electron–electron interactions at A and B sublattices. To calculate susceptibility, we evaluate the two-particle electron Green’s function by using Zubarev’s Green’s function technique. The frequency-dependent real part of antiferromagnetic susceptibility of the system is computed numerically by taking $$1000 \times 1000$$ grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher energy peak appearing at substrate-induced gap. The evolution of these two peaks is investigated by varying neutron wave vector, Coulomb correlation energy, substrate-induced gap, electron hopping integrals and A- and B-site electron doping concentrations.

Dielectric constant of graphene-on-polarized substrate: A tight-binding model study

We report here a microscopic tight-binding theoretical study of the dynamic dielectric response of graphene-on-polarizable substrate with impurity. The Hamiltonian consists of first, second and third nearest-neighbour electron hopping interactions besides doping and substrate-induced effects on graphene. We have introduced electron–electron correlation effect at A and B sublattices of graphene which is considered within Hartree–Fock mean-field approximation. The electron occupancies at both sublattices are calculated and solved self-consistently and numerically for both up- and down-spin orientations. The polarization function appearing in the dielectric function is a two-particle Green’s function which is calculated by using Zubarev’s Green’s function technique. The temperature and optical frequency-dependent dielectric function is evaluated and compared with experimental data by varying Coulomb correlation energy, substrate-induced gap and impurity concentrations.

Tight-Binding Model Study of Anti-ferromagnetic Order in AA-Stacked Bi-layer Graphene

We address here the anti-ferromagnetic order present in AA-stacked bi-layer graphene in a transversely applied electric field. The system is described by kinetic energy with nearest-neighbor electron hopping with same hopping integral t 1 for both the layers. Besides this, Coulomb interaction exists at A and B sub-lattices with same Coulomb correlation energy. The electron Green’s functions are calculated by Zubarev’s Green’s technique. The temperature-dependent anti-ferromagnetic magnetization is calculated from the Green’s function and is computed numerically and self-consistently. The strong on-site Coulomb interaction stabilizes the anti-ferromagnetic order in graphene. We assume that the electron spin at A site in the first layer is directed in the opposite direction to that of A site electron in the second layer. Similar spin order is observed for electrons in B site atom in reversed order. It is observed that anti-ferromagnetic (AFM) magnetization in the first layer nearly remains constant up to certain temperature and then increases with temperature, while the AFM magnetization in the second layer remains nearly constant and then rapidly decreases with temperature. The net AFM magnetization in bi-layer graphene remains constant and then rapidly increases with temperature. The evolution of the AFM magnetization is studied by varying transverse electric field, Coulomb energy, and temperature.

Weak orbital ordering of Irt2gstates in the double perovskiteSr2CeIrO6

The electronic and magnetic properties of monoclinic double perovskite Sr$_2$CeIrO$_6$ were examined based on both experiments and first-principles density functional theory calculations. From the calculations we conclude that low-spin-state Ir$^{4+}$ (5$\textit{d}^5$, S=$\frac{1}{2}$) shows t$_{2g}$ band derived anti-ferro type orbital ordering implying alternating occupations of $\textit{d}_{yz}$ and $\textit{d}_{xz}$ orbitals at the two symmetrically independent Ir sites. The experimentally determined Jahn-Teller type distorted monoclinic structure is consistent with the proposed orbital ordering picture. Surprisingly, the Ir-5$\textit{d}$ orbital magnetic moment was found to be $\approx$ 1.3 times larger than the spin magnetic moment. The experimentally observed AFM-insulating states are consistent with the calculations. Both electron-electron correlation and spin-orbit coupling (SOC) are required to drive the experimentally observed AFM-insulating ground state. This single active site double perovskite provides a rare platform with a prototype geometrically frustrated fcc lattice where among the different degrees of freedom (i.e spin, orbital, and lattice), spin-orbit interaction and Coulomb correlation energy scales compete and interact with each other.

Surface-induced spin state locking of the [Fe(H2B(pz)2)2(bipy)] spin crossover complex

Temperature- and coverage-dependent studies of the Au(1 1 1)-supported spin crossover Fe(II) complex (SCO) of the type [Fe(H2B(pz)2)2(bipy)] with a suite of surface-sensitive spectroscopy and microscopy tools show that the substrate inhibits thermally induced transitions of the molecular spin state, so that both high-spin and low-spin states are preserved far beyond the spin transition temperature of free molecules. Scanning tunneling microscopy confirms that [Fe(H2B(pz)2)2(bipy)] grows as ordered, molecular bilayer islands at sub-monolayer coverage and as disordered film at higher coverage. The temperature dependence of the electronic structure suggest that the SCO films exhibit a mixture of spin states at room temperature, but upon cooling below the spin crossover transition the film spin state is best described as a mix of high-spin and low-spin state molecules of a ratio that is constant. This locking of the spin state is most likely the result of a substrate-induced conformational change of the interfacial molecules, but it is estimated that also the intra-atomic electron–electron Coulomb correlation energy, or Hubbard correlation energy U, could be an additional contributing factor.

Electronic structure of the unoccupied electron energy states in FeSe1−xTex

Abstract Inverse photoemission spectroscopic (IPES) measurements along with LDA based band structure calculations have been used to investigate the unoccupied electronic structure of FeSe1−xTex system. The observed doping and temperature dependent pseudogap in this system is found to be linked to the change in the chalcogen height in their geometric structure. The depletion in spectral weight from the near EF states at low temperature in IPES has been correlated with the enhancement of the 3z2–r2 orbitals in the photoemission spectroscopy (PES). The Coulomb correlation energy U, estimated from the combined PES and IPES spectra, signifies the enhancement in electron correlations in FeSe1−xTex, with doping. The formation of pseudogap in PES and IPES confirms the importance of correlations in the 11 family of Fe superconductors.

Spin polarization of nucleons: Limits of low and high temperatures

The problem of explaining the origin of the magnetic fields of white dwarfs with hydrogen envelopes and of type II supernovae via the spin polarization of nucleons is considered. The question of the ferromagnetism of an electron-nucleon system with contact nuclear spin-isospin-dependent interaction is considered at densities two and more orders of magnitude lower than the nuclear saturation density at high and low temperatures using the minimum of energy density at finite degrees of spin polarization and the Stoner criterion. The importance of considering Coulomb exchange and correlation energy is shown. The initiation of spin polarization is found to be energetically advantageous at proton and neutron densities on the orders of 1030–1031 cm−3 and 1035–1036 cm−3. The first region of densities is shown to exist due to the Coulomb exchange energy, the effect of which is reduced by the Coulomb correlation energy.

Estimate of the Coulomb correlation energy in CeAg2Ge2 from inverse photoemission and high resolution photoemission spectroscopy

The occupied and the unoccupied electronic structure of CeAg2Ge2 single crystal has been studied using high resolution photoemission and inverse photoemission spectroscopy, respectively. High resolution photoemission reveals the clear signature of Ce 4f states in the occupied electronic structure which was not observed clearly in our earlier studies. The Coulomb correlation energy in this system has been determined experimentally from the position of the 4f states above and below the Fermi level. Theoretically, the correlation energy has been determined by using the first principles density functional calculations within the generalized gradient approximations taking into account the strong intra-atomic (on-site) interaction Hubbard Ueff term. The calculated valence band shows minor changes in the spectral shape with increasing Ueff due to the fact that the density of Ce 4f state is narrow in the occupied part and is hybridized with the Ce 5d, Ag 4d and Ge 4p states. On the other hand, substantial changes are observed in the spectral shape of the calculated conduction band with increasing Ueff since the density of Ce 4f state is very large in the unoccupied part, compared to other states. The estimated value of correlation energy for CeAg2Ge2 from the experiment and the theory is ≈ 4.2 eV. The resonant photoemission data are analyzed in the framework of the single-impurity Anderson model which further confirms the presence of the Coulomb correlation energy and small hybridization in this system.

Structural Distortion in Antiferromagnetic BaFe2As2 as a Result of Time-Inversion Symmetry

As reported by Q. Huang et al. (Phys. Rev. Lett. 101, 257003, 2008), neutron diffraction studies show an onset of antiferromagnetic order in BaFe2As2 associated with a tetragonal-to-orthorhombic distortion. We determine the group Cmca as the space group of antiferromagnetic BaFe2As2 and identify a roughly half-filled energy band of BaFe2As2 with Bloch functions of special symmetry as magnetic band. As explained by the group-theoretical nonadiabatic Heisenberg model, the electrons in this narrow band may lower their Coulomb correlation energy by producing just the experimentally observed antiferromagnetic state if this state does not violate group-theoretical principles. However, in undistorted BaFe2As2 the time-inversion symmetry of the system interferes with the stability of the antiferromagnetic state. Nevertheless, it can be stabilized by a structural distortion of BaFe2As2 going beyond the magnetostriction. We derive two possible structural distortions stabilizing the antiferromagnetic state. These distortions are described by their space groups and consist in mere displacements of the Fe atoms.

Intrinsic correlated electronic structure of CrO2revealed by hard x-ray photoemission spectroscopy

Bulk-sensitive hard x-ray photoemission spectroscopy (HAXPES) reveals for as-grown epitaxial films of half-metallic ferromagnetic CrO2(100) a pronounced screening feature in the Cr 2p3/2 core level and an asymmetry in the O 1s core level. This gives evidence of a finite, metal-type Fermi edge, which is surprisingly not observed in HAXPES. A spectral weight shift in HAXPES away from the Fermi energy is attributed to single-ion recoil effects due to high energy photoelectrons. In conjunction with inverse PES the intrinsic correlated Mott-Hubbard-type electronic structure is unravelled, yielding an averaged Coulomb correlation energy Uav ~ 3.2 eV.

First-principles study of the electronic structure and optical properties of UO2

The electronic structure and optical properties of UO2 are investigated using the first principles density functional method within local-spin density approximation (LSDA), and the Coulomb correlation energy (U) is used to calculate the lattice constant, energy band structure and optical properties of UO2. The calculated lattice constant is 5.40 ?, and the band gap is 1.82 eV. We succeeded in predicting the correct anti-ferromagnetic insulating ground state of uranium dioxide. By analyzing the energy structure and dielectric function, we find that in uranium ions the 6d band splits into two sub-bands, which is in agreement with experimental results.

Generalized Slater-Jastrow trial function: Application to the electron gas at high density

The function $u(i,j)=u(|{\mathbf{r}}_{i}\ensuremath{-}{\mathbf{r}}_{j}|)$, in terms of which variational trial functions of the Slater-Jastrow type are expressed, is generalized to include dependence on the electron momenta as well as on the electron-pair separations. The resulting Euler equations are used to evaluate the ground-state coulomb correlation energy giving ${ϵ}_{c}=0.0622\text{ }\text{log}({r}_{s})\ensuremath{-}0.1441\text{ }\text{Ry}$, where ${r}_{s}$ is the ratio of the radius of a sphere, containing, on average one electron, to the Bohr radius. This correlation energy is 0.050 Ry lower than the corresponding result ${ϵ}_{c}=0.0622\text{ }\text{log}({r}_{s})\ensuremath{-}0.094\text{ }\text{Ry}$ found by Gell-Mann and Brueckner. Also evaluated are the corresponding correlation corrections to the Hartree-Fock (HF) exchange potential energy and to the average exchange charge density as a function of distance. The correction to the HF exchange potential energy is shown to cancel the divergence of the HF exchange energy at the Fermi energy so that the electron effective mass remains finite.